Question

The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow a normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 308 days with a standard deviation of 12 days. A hypothesis test is undertaken to determine whether the modification increased the battery life. What is the value of the test statistic for the hypothesis test?

Answer 1

DATE * let x= battery life we have given that 2= 308 days and u= 305 day's Here we have to test n = 20 s = 12 days Ho: u = 305 M> 305 ie the battery life is 305 days the modification increased the battery life statistic i-o Under Ho the test IS t X - N tn-idof 308 - 305 121 zo 1.1180 The value of test statistic is for the given hypothesis test. is loo X = number of students reply that calutus their favorite subject - n= sample size= 225 Å= proportion of student reply that calculus is their favorite subjed among 225 students among the = 0.4444 n 225 CS Scanned with CamScanner

DATE As we know loo(1-2) % confidence interval for population proportion p is given as ( Å Zolly J î (li Å + Zatz Jô clips Here have to find 95% confidence interal so 24/2 = 2005 - 20.025=1.96 Å - Zarz / a (1-pl :: lower bound for c. I 0.4444-(1.96 Jouuu 444 (1-0.604) 225 =0.38 to + Z42 upper bound for CI JACI (1-96 0.4444 + 1.96x louuuull-0.4444) 225 0.51 95% confidence interval for the proportion of all students taking calculus who considered it their favorite subjed is (0.38 0.51) cs Scanned with CamScanner

* we have given that n-25, 8 =12 si 15 we know lool 1-2% confidence interval for mean when population variance is unknown tn-idla s et tn-l 42 s Jn Jh 1 Here we have to find 95% confidence interval for mean - tnit 22 = +251 0.05. t24 0.025 = 2.064 .: lower bound - th-idla slun 2-064 x 15 525 5.808 upper bound etthin 2/2 12+(2.064 x 15 as 18-192 95% confidence interval for mean is ( 5.808 18.192) CS Scanned with CamScanner

t table as follows:

7:43 62.0 KB/S 774 Edit 26 Х t-distribution Confidence Level 85% 90% 95% 98% 60% 70% 80% 99% 99.8% 99.9% 2 Tailed 1 Tailed 0.40 0.20 0.30 0.15 0.20 0.10 Level of Significance 0.15 0.10 0.05 0.02 0.075 0.05 0.025 0.01 0.01 0.005 0.002 0.001 0.001 0.0005 26.30 12.39 8.499 6.835 5.946 5.403 5.039 0.039 4.780 2.822 3.250 df 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 18 19 20 21 22 23 24 25 4.586 4.437 1.376 1.963 3.133 4.195 6.320 12.69 31.81 63.67 1.060 1.385 1.883 2.278 2.912 4.271 4.271 6.816 9.520 0.978 1.250 1.637 1.924 2.352 3.179 4.525 5.797 0.941 1.190 1.533 1.778 2.132 2.776 3.744 4.596 0.919 1.156 1.476 1.699 2.015 2.570 3.365 4.030 0.906 1.134 1.440 1.650 1.943 2.447 3.143 3.707 0.896 1.119 1.415 1.617 1.895 2.365 2.999 3.500 0.889 1.108 0.00% 1.397 1.592 1.860 2.306 2.897 3.356 0.000 0.883 1.100 1.383 1.574 1.833 2.262 0.879 1.372 1.093 V. 1.559 1.813 2.228 2.764 3.170 0.875 0.00 1.088 1.363 1.305 1.548 1.796 2.201 2.719 3.106 0.873 1.083 1.356 1.538 1.782 2.179 2.682 3.055 0.870 1.079 1.350 1.530 1.771 2.160 2.651 3.013 0 000 0.868 1.076 1.345 1.523 1.761 . 15 2.145 2.625 2.977 0.866 1.074 1.341 1.517 1.753 2.131 2.603 2.947 0.865 1.071 1.337 1.512 1.746 2.120 2.584 2.921 0.863 1.069 1.333 1.508 1.740 2.110 2.567 2.899 0.862 1.067 1.330 1.504 1.734 2.101 2.553 2.879 0.861 1.000 1.066 1.328 1.500 1.000 1.729 2.095 2.093 2.540 2.861 0.860 1.064 1.325 1.497 19 1.725 .125 2.086 2.529 2.840 0.859 1.063 1.323 1.494 1.721 2.080 2.518 2.832 0.858 1.061 1.321 1.717 2.074 2.074 2.509 2.819 0.857 1.060 1.319 1.489 1.714 2.069 2.500 2.808 0.857 1.487 1.711 2.064 2.493 2.797 0.856 1.058 1.485 1.708 2.060 2.486 2.788 0.856 1.058 1.315 1492 1.483 1.706 2.056 2.479 2.779 0.855 1.057 1.314 ora 1.482 1.703 2.052 2.473 more 2.473 2.771 1994 0.855 1.056 1.313 1.480 1.701 2.048 2.468 2.764 MORALES 1120 1.055 Icon 0.854 1.311 1.479 1.699 2.045 2.463 2.757 LE 0.854 1.055 1.310 2019 20 1.477 1.697 Movie 2.042 2.458 2.750 0.851 1.050 1.303 Tied 10 201 202 203 1.468 1.684 2.021 2.424 2.705 dou 0 0 100 0.849 1.047 1.299 1.462 1.676 2.009 2.404 2.678 0.848 0 1 1.045 1.296 1.458 1.671 2.000 2.391 2.661 0.847 1.044 1.294 1.456 1.667 1.994 2.381 2.648 0.846 1.043 1.292 1.453 1.664 1.990 2.374 2.639 0.846 1.042 1.291 1.452 1.662 1.987 2.369 2.632 0.845 1.042 1.290 1.451 1.660 1.984 2.365 2.626 19.65 9.937 7.115 5.876 5.201 4.783 4.500 4.297 4.297 4.144 4.025 3.930 3.930 3.852 3.788 3.733 3.687 3.646 3.611 3.580 4.318 4.221 4.141 4.073 4.015 3.965 3.922 3.884 3.850 3.552 3.820 1.492 1.059 1.318 1.316 27 28 29 30 40 50 60 70 80 90 100 3.528 3.505 3.485 3.467 3.451 3.435 3.421 3.409 3.397 3.386 3.307 3.262 3.232 3.211 3.196 3.184 3.174 3.792 3.768 3.746 3.725 2707 3.707 con 3.690 3.674 3.660 3.646 3.551 3.496 3.460 10 3.435 3.417 3.402 3.391 0842 1.036 1.282 1.440 1.645 1.960 2.327 2.576 3.091 3.291 סס w DD Tools Mobile View Share PDF to DOC

z value table as follows:

The following table shows the critical values, Zy of Z at commonly ised level of significance for both two tailed and one tailed tests. Level of Significance Tests 5% i.e. a = 0.05 1% i.e. a = 0.01 10% i.e. a = 0.1 Two tailed -1.645 and -1.96 and 1.96 -2.58 and 2.58 tests 1.645 Right tailed tests 1.645 2.33 1.28 Left tailed tests -1.645 -2.33 -1.28 cs So with Care cs Scanned with CamScanner